Looking for ideas on how to efficiently clean the heat exchanger flame portion of the refrigerator. (1965 Caravel with Dometic, gas only.)

The air-fuel mixture adjusting rings vibrated loose, causing the propane to create black carbon on the inside of the "generator" portion of the back of the refrigerator. The drawer above the refrigerator is removable. Blowing air from the top of the refrigerator to the bottom may be an option. Placing a shop vacuum at the flame / burner area may collect some of the debris. Cleaning products, other ideas, or experiences?